At this point I use only the AI curves in combination with the Polyextrude SOP. The problem with your AI file is: You have 13 single shapes and the Extrude effects the curves separately.
Additional some of the points overlap. You have to connect the curves to one single shape. Additional you should split the part on the left side and export a second AI curve. I recommend to export only the half of the curve and use the Mirror SOP to create the full object. The points in the middle maybe overlap with the rest of the curve and cause problems with the Polyextrude SOP. I haven't split the second curve in the example.
I added some more points in the AI file at the round parts of the logo. The curves are not clean.
ai_example.zip